Question

Write an equation for the line that passes through the points (6,6) and (12,9)

Answer 1

A line is represented by the following expression in slope-intercept form:

`\begin{gathered} y=mx+b \\ \text{where, } \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

To get this expression, we must calculate the slope first and then use the slope-point form to finally get the slope-intercept form:

*Slope is given by this formula:

Using the two given points (6,6) and (12,9)

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the points:

`\begin{gathered} m=(9-6)/(12-6) \\ m=(3)/(6) \\ m=(1)/(2) \end{gathered}`

Then, by the slope-point form, which is given by:

`y-y_1=m(x-x_1)`
`\begin{gathered} y-6=(1)/(2)(x-6) \\ y=(1)/(2)x-3+6 \\ y=(1)/(2)x+3 \end{gathered}`